This class manages ("wraps") a pointer to an int. All resources should be wrapped in some fashion, for cleanliness (no explicit clean up code or noise) and correctness (destructor is guaranteed to run; cannot forget to clean up, and safe with exceptions).

This pattern is called Scoped-bound Resource Management (SBRM), though a far more common (but most esoteric) name is Resource-Acquisition is Initialization (RAII). The idea is to bind a resource's clean-up to a destructor, for the reasons given above: the scope handles the rest.

Note that I said it was missing a copy-constructor and copy-assignment operator. This is due to the Rule of Three. (See linked question for detailed explanation.) The simplest way to correctly implement this rule is with the copy-and-swap idiom, explained here.

Sometimes, it's not pragmatic to write wrapper class for resource clean-up, usually when the resource is unique or used once. (Or with transactional programming.) The solution to this is called scope guard, a way of writing clean-up code inside the function that needs it.

You may find more information by searching for it in your favorite search provider (that is, Google), or going to the "primary" document here. Note that Boost provides a utility for this, as it usually does for good idioms.

A wrapper is just some smallish class whose purpose is to provide a different interface than the thing it wraps. For example, it is common to take a C API and write one or more classes that "wrap" it to provide an object-oriented interface rather than a procedural one.

You asked for circumstances of writing wrapper classes.For example, if you are in a company that makes use of different types of cameras, let us say USB, firewire etc. Each of the manufacturers will provide a different set of functions through an API to start the camera, set the parameters and read the image stream from it.

Now the programmer who builds the applications in your company need to be insulated from all the specific details in the various APIs. Now, what you can do is write a wrapper class around the APIs for each of the cameras or smarter, just one class with simple functions, wrapping around the existing code provided by the API.

For instance, we can design classes
MyUSBCameraWrapperClass,
MyFirewireCameraWrapperClass
with some member functions like
setFrameRate(int fps),
getImgFrame(*framebuffer), etc.

The programmers in your company can then use MyUSBCameraWrapperClass usbcam; usbcam.setFrameRate(30), etc. You get the point??

A wrapper class is a class that wraps a functionality with another interface.

Suppose you have the function f():

void f() { std::cout << "hello\n"; }

A simple wrapper class might be

class C {
f() { std::cout << "hello\n"; }
};

You might write a wrapper when your existing codebase expects a particular interface. This is the essence of the adapter design pattern. Or you might wrap a function in a class if you wish to maintain state for that function. Or you might wrap a function in a class' constructor or destructor if you want it to conveniently and automatically be called for you in a correct and deterministic manner. And the list goes on.

The resource wrapper makes certain, that compiler generated code worries about the destruction of the resource created by the constructor via what is today called RAII. It is easy to combine such classes via base/member class relationships into complex classes.
In case of the creation function fails, a system error exception is thrown, providing rich error information about the error.

The functional wrapper is used instead of the plain OS function. Also in case of failure a system exception is being thrown.

This way somebody using my code doesn't need a debugger and debug code to find out what is failing in a complex environment with many libraries and processes and remote machines.

Also these wrappers provide some OS abstraction -- the code using them does not have to worry about OS differences.